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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

On the undetected error probability of a concatenated coding scheme for error control

Consider a concatenated coding scheme for error control on a binary symmetric channel, called the inner channel. The bit error rate (BER) of the channel is correspondingly called the inner BER, and is denoted by Epsilon (sub i). Two linear block codes, C(sub f) and C(sub b), are used. The inner code C(sub f), called the frame code, is an (n,k) systematic binary block code with minimum distance, d(sub f). The frame code is designed to correct + or fewer errors and simultaneously detect gamma (gamma +) or fewer errors, where + + gamma + 1 = to or d(sub f). The outer code C(sub b) is either an (n(sub b), K(sub b)) binary block with a n(sub b) = mk, or an (n(sub b), k(Sub b) maximum distance separable (MDS) code with symbols from GF(q), where q = 2(b) and the code length n(sub b) satisfies n(sub)(b) = mk. The integerim is the number of frames. The outercode is designed for error detection only.

Deng, H.↗
NASA NTRS1984

Probability of undetected error after decoding for a concatenated coding scheme

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Costello, D. J., Jr.↗
NASA NTRS1984

Undetected error probability and throughput analysis of a concatenated coding scheme

The performance of a proposed concatenated coding scheme for error control on a NASA telecommand system is analyzed. In this scheme, the inner code is a distance-4 Hamming code used for both error correction and error detection. The outer code is a shortened distance-4 Hamming code used only for error detection. Interleaving is assumed between the inner and outer codes. A retransmission is requested if either the inner or outer code detects the presence of errors. Both the undetected error probability and the throughput of the system are analyzed. Results indicate that high throughputs and extremely low undetected error probabilities are achievable using this scheme.

Costello, D. J.↗
NASA NTRS1985

A concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8)).

Lin, S.↗
NASA NTRS1985

A concatenated coding scheme for error control

A concatenated coding scheme for error contol in data communications was analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughout efficiency of the proposed error control scheme incorporated with a selective repeat ARQ retransmission strategy is analyzed.

Lin, S.↗
NASA NTRS1986

A concatenated coding scheme for error control

In this paper, a concatenated coding scheme for error control in data communications is presented and analyzed. In this scheme, the inner code is used for both error correction and detection; however, the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error (or decoding error) of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughput efficiency of the proposed error control scheme incorporated with a selective-repeat ARQ retransmission strategy is also analyzed. Three specific examples are presented. One of the examples is proposed for error control in the NASA Telecommand System.

Kasami, T.↗
NASA NTRS1988

VLA telemetry performance with concatenated coding for Voyager at Neptune

Current plans for supporting the Voyager encounter at Neptune include the arraying of the Deep Space Network (DSN) antennas at Goldstone, California, with the National Radio Astronomy Observatory's Very Large Array (VLA) in New Mexico. Not designed as a communications antenna, the VLA signal transmission facility suffers a disadvantage in that the received signal is subjected to a gap or blackout period of approximately 1.6 msec once every 5/96 sec control cycle. Previous analyses showed that the VLA data gaps could cause disastrous performance degradation in a VLA stand-alone system and modest degradation when the VLA is arrayed equally with Goldstone. New analysis indicates that the earlier predictions for concatenated code performance were overly pessimistic for most combinations of system parameters, including those of Voyager-VLA. The periodicity of the VLA gap cycle tends to guarantee that all Reed-Solomon codewords will receive an average share of erroneous symbols from the gaps. However, large deterministic fluctuations in the number of gapped symbols from codeword to codeword may occur for certain combinations of code parameters, gap cycle parameters, and data rates. Several mechanisms for causing these fluctuations are identified and analyzed. Even though graceful degradation is predicted for the Voyager-VLA parameters, catastrophic degradation greater than 2 dB can occur for a VLA stand-alone system at certain non-Voyager data rates inside the range of the actual Voyager rates. Thus, it is imperative that all of the Voyager-VLA parameters be very accurately known and precisely controlled.

Dolinar, S. J., Jr.↗
NASA NTRS1989

Performance of concatenated codes using 8-bit and 10-bit Reed-Solomon codes

The performance improvement of concatenated coding systems using 10-bit instead of 8-bit Reed-Solomon codes is measured by simulation. Three inner convolutional codes are considered: (7,1/2), (15,1/4), and (15,1/6). It is shown that approximately 0.2 dB can be gained at a bit error rate of 10(-6). The loss due to nonideal interleaving is also evaluated. Performance comparisons at very low bit error rates may be relevant for systems using data compression.

Pollara, F.↗
NASA NTRS1991

Frame error rate of the NASA concatenated coding system

For a concatenated coding system, the effect of interleaving depth on interleaved frame-error rate is compiled by simulation. Comparisons are made for three different inner convolutional codes; all three systems have a (255,223) 8-bit Reed-Solomon code as an outer code. For all the inner convolutional codes tested, an interleaving depth smaller that 4 causes substantial loss.

Swanson, L.↗
NASA NTRS1990

Performance of concatenated Reed-Solomon trellis-coded modulation over Rician fading channels

A concatenated coding scheme for providing very reliable data over mobile-satellite channels at power levels similar to those used for vocoded speech is described. The outer code is a shorter Reed-Solomon code which provides error detection as well as error correction capabilities. The inner code is a 1-D 8-state trellis code applied independently to both the inphase and quadrature channels. To achieve the full error correction potential of this inner code, the code symbols are multiplexed with a pilot sequence which is used to provide dynamic channel estimation and coherent detection. The implementation structure of this scheme is discussed and its performance is estimated.

Moher, Michael L.↗
NASA NTRS1995

Testing the performance of feedback concatenated decoder with a nonideal receiver

One of the inherent problems in testing the feedback concatenated decoder (FCD) at our operating symbol signal-to-noise ratio (SSNR) is that the bit-error rate is so low that we cannot measure it directly through simulations in a reasonable time period. This article proposes a test procedure that will give a reasonable estimate of the expected losses even though the number of frames tested is much smaller than needed for a direct measurement. This test procedure provides an organized robust methodology for extrapolating small amounts of test data to give reasonable estimates of FCD loss increments at unmeasurable miniscule error rates. Using this test procedure, we have run some preliminary tests on the FCD to quantify the losses due to the fact that the input signal contains multiplicative non-white non-Gaussian noises resulting from the buffered telemetry demodulator (BTD). Besides the losses in the BTD, we have observed additional loss increments of 0.3 to 0.4 dB at the output of the FCD for several test cases with loop signal-to-noise ratios (SNR's) lower than 20 dB. In contrast, these loss increments were less than 0.1 dB for a test case with the subcarrier loop SNR at about 28 dB. This test procedure can be applied to more extensive test data to determine thresholds on the loop SNRs above which the FCD will not suffer substantial loss increments.

Feria, Y.↗
NASA NTRS1996

Bounds on Block Error Probability for Multilevel Concatenated Codes

Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.

Lin, Shu↗
NASA NTRS1997

Investigation of the Use of Erasures in a Concatenated Coding Scheme

A new method for declaring erasures in a concatenated coding scheme is investigated. This method is used with the rate 1/2 K = 7 convolutional code and the (255, 223) Reed Solomon code. Errors and erasures Reed Solomon decoding is used. The erasure method proposed uses a soft output Viterbi algorithm and information provided by decoded Reed Solomon codewords in a deinterleaving frame. The results show that a gain of 0.3 dB is possible using a minimum amount of decoding trials.

Kwatra, S. C.↗
NASA NTRS1997

Multidimensional Trellis Coded Phase Modulation Using a Multilevel Concatenation Approach: Code Design - Part 1

The first part of this paper presents a simple and systematic technique for constructing multidimensional M-ary phase shift keying (MMK) trellis coded modulation (TCM) codes. The construction is based on a multilevel concatenation approach in which binary convolutional codes with good free branch distances are used as the outer codes and block MPSK modulation codes are used as the inner codes (or the signal spaces). Conditions on phase invariance of these codes are derived and a multistage decoding scheme for these codes is proposed. The proposed technique can be used to construct good codes for both the additive white Gaussian noise (AWGN) and fading channels as is shown in the second part of this paper.

Rajpal, Sandeep↗
NASA NTRS1996

New Bandwidth Efficient Parallel Concatenated Coding Schemes

We propose a new solution to parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2 bits/sec/Hz with 8PSK and 16QAM signal constellations.

trellis codes multilevel amplitude modulations dec↗